MIT 18.100B Real Analysis, Spring 2025 - Lecture 18: Integrable Functions

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG We will show that continuous functions are integrable. This means that the graph of such a function bound a well defined area. To do so, we define what it means for a function to be uniformly continuous. This is a strong version of continuity but we will see that all continuous functions on a closed and bounded interval have this stronger property. Once we have shown that all continuous functions on a compact interval are uniformly continuous, it will follow relatively easily that they are integrable. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.